Asymptotic Behavior of a Nonparametric Estimator of the Renewal Function for Random Fields-Reference-Cited by-同舟云学术

Asymptotic Behavior of a Nonparametric Estimator of the Renewal Function for Random Fields

Published:2023-09-24 Issue:19 Volume:11 Page:4048
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Andriamampionona Livasoa¹,Harison Victor¹,Harel Michel²³⁴

Affiliation:

1. Department of Mathematics and Informatics, University of Antananarivo, Antananarivo 101, Madagascar

2. INSPÉ de Limoges, Université de Limoges, 87036 Limoges, CEDEX 3, France

3. Institut de Mathématiques de Toulouse, UMR5219 UPS, 31062 Toulouse, CEDEX 9, France

4. Laboratoire Vie-Santé, UR 24 134, Faculté de Médecine, 87025 Limoges, France

Abstract

In this paper, we study the asymptotic normality of a nonparametric estimator of the renewal function associated with a sequence of absolutely continuous nonnegative two-dimensional random fields. We prove that this estimator is asymptotically unbiased. The asymptotic normality of this estimator is established.

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Link

https://www.mdpi.com/2227-7390/11/19/4048/pdf

Reference14 articles.

1. Nonparametrical renewal function estimation;Frees;Ann. Stat.,1986

2. Asymptotics of the sample renewal function;Harel;J. Math. Anal. Appl.,1995

3. Weak convergence of nonparametric estimators of the multidimensional and multidimensional-multivariate renewal functions on Skorohod topology spaces;Harel;Stat. Inference Stoch. Processes,2022

4. Nonparametric estimation of the renewal function by empirical data;Markovich;Stoch. Model.,2006

5. Nonparametric estimation in renewal theory I: The empirical renewal function;Grubel;Ann. Stat.,1993

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